Exciton molecules in multi-valley semiconductors

Abstract

The structure of exciton molecules depends essentially on the number of valleys in the conduction and valence bands. The anisotropy of electron and hole effective masses is also important. In the simplest case, both the conduction and the valence bands have only one valley each, the electron and hole effective masses are isotropic and only biexcitons and an insulating exciton liquid can exist. For multi-valley semiconductors, such as Ge, Si, AlAs, AlSb, AlN, and many solid solutions of these semiconductors, it is shown both experimentally and theoretically that: (i) there may exist exciton molecules, such as biexcitons, triexcitons, tetraexcitons, and (ii) the exciton condensate is always metallic, furthermore, the metalic liquid has an anomalously high density. The reason for such behavior is clear enough. In the multi-valley semiconductors, there are many electrons and holes occupying a 1s-state, because there is an additional quantum number, the number of the valley. For example, in silicon up to 12 electrons may occupy six different valleys, but all these electrons may be in the 1s-state (spin-up ↑ and spin-down ↓ in each valley). The largest possible number of holes in the exciton molecule is four (± 3 2 and ± 1 2 spins). In silicon, the following exciton molecules may exist: biexcitons, triexcitons, and tetraexcitons. The tetraexciton molecules are more strongly bound and have a smaller radius as compared with the triexciton or biexciton molecules. This review discusses the question of whether or not some new stable and more strongly bound exciton molecules consisting of 11 or 12 excitons can exist. These molecules would have four holes in the 1s-state and seven or eight holes in 2s- and 2p-states. All electrons in such a molecule would occupy the 1s-state. Exciton molecules captured by quantum dots are also considered. The binding energy of excitons in these molecules is much higher than that of a free exciton. In GaP, a quantum dot can bind either only one electron or only one hole with a very low binding energy, but the binding energy of the exciton molecule may reach 5Ry ex, or even higher. The electron ground state in quantum dots is sixfold degenerate, because the “camel-back” structure of the conduction band is shallow enough. The radius of the exciton molecule captured by a quantum dot is smaller than that of a free molecule. The complexity of the exciton molecules is based on the fact that these molecules consist of up to six different electrons and six different holes, because the spin–orbit interaction in the valence band is small, and the “camel-back” structure in the conduction band is shallow.